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I think of it as "Could Newton have used this to find the expressions for the forces he was analyzing (eg gravitational force = g m_1 m_2 / d^2)?". I once asked

by t_mann 2y ago

I think of it as "Could Newton have used this to find the expressions for the forces he was analyzing (eg gravitational force = g m_1 m_2 / d^2)?". I once asked a physics prof whether that was conceivable in principle, and he said yes. It seems to me like KANs should be able to find expressions like these given experimental data. If that was true, then I don't see how that wouldn't deserve being called interpretability.

fjkdlsjflkds 2y ago
> It seems to me like KANs should be able to find expressions like these given experimental data. Perhaps, but this is not something unique to KANs: any symbolic regression method can (at least in theory) find such simple expressions. Here is an example of such type of work (using non-KAN neural networks): https://www.science.org/doi/10.1126/sciadv.aay2631 https://www.science.org/doi/10.1126/sciadv.aay2631 Rephrasing: just because you can reach simple expressions with symbolic regression methods based on neural networks (or KANs) does not necessarily imply that neural networks (or KANs) are inherently interpretable (particularly once you start stacking multiple layers).
nathan_compton 2y ago
Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation.
- t_mann 2y ago
  It seems like you're asking for quite a lot here. Are there any examples of common interpretable ML methods that would give you anything like that answer? The most common methods that are called interpretable would give you hints like "Mass and distance matter for gravity, color doesn't" or "Gravity gets stronger with mass and weaker with distance". Both are clearly less informative than the formula. The only way I could think of to get anywhere near such an answer would be to use symbolic regression first and then ask an LLM to interpret the result. And that would probably take quite some more original research to get it anywhere near working, and even then probably primarily for problems where the answer is already known. I agree that this kind of answer would be useful, but we also have to be honest that that's not what currently meant by interpretability. And that's what should matter for evaluating the claim - it's not misleading if it delivers what one can reasonably expect. Whether we should update our interpretability definitions is a different (interesting) discussion.
- dataflow 2y ago
  > Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation. I used to think the same, but don't the weak and strong forces decay differently?
  - nathan_compton 2y ago
    Sort of, but the same sort of thinking is involved in both at a fundamental level. Most of the coefficients in a QFT expansion can almost be guessed by just considering dimensional analysis. Like the "force laws" of those two theories derive from the dimensionality of space time, the symmetry group involved (which is itself just an irreducible representation of rotations in the spacetime) and then some details having to do with symmetry breaking and the fact that gluons carry charge. Not that all of that is simple, but it doesn't invalidate the logic which gives us the 1/r^2 force law in the classical regimes of gravity and E&M.

by t_mann 2y ago

fjkdlsjflkds 2y ago

> It seems to me like KANs should be able to find expressions like these given experimental data. Perhaps, but this is not something unique to KANs: any symbolic regression method can (at least in theory) find such simple expressions. Here is an example of such type of work (using non-KAN neural networks): https://www.science.org/doi/10.1126/sciadv.aay2631 https://www.science.org/doi/10.1126/sciadv.aay2631 Rephrasing: just because you can reach simple expressions with symbolic regression methods based on neural networks (or KANs) does not necessarily imply that neural networks (or KANs) are inherently interpretable (particularly once you start stacking multiple layers).

nathan_compton 2y ago

Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation.

t_mann 2y ago
It seems like you're asking for quite a lot here. Are there any examples of common interpretable ML methods that would give you anything like that answer? The most common methods that are called interpretable would give you hints like "Mass and distance matter for gravity, color doesn't" or "Gravity gets stronger with mass and weaker with distance". Both are clearly less informative than the formula. The only way I could think of to get anywhere near such an answer would be to use symbolic regression first and then ask an LLM to interpret the result. And that would probably take quite some more original research to get it anywhere near working, and even then probably primarily for problems where the answer is already known. I agree that this kind of answer would be useful, but we also have to be honest that that's not what currently meant by interpretability. And that's what should matter for evaluating the claim - it's not misleading if it delivers what one can reasonably expect. Whether we should update our interpretability definitions is a different (interesting) discussion.
dataflow 2y ago
> Just giving the force law hardly counts as interpret-ability. You probably know that the 1/r^2 in the force law comes from the dimensionality of space. That is the interpretation. I used to think the same, but don't the weak and strong forces decay differently?
- nathan_compton 2y ago
  Sort of, but the same sort of thinking is involved in both at a fundamental level. Most of the coefficients in a QFT expansion can almost be guessed by just considering dimensional analysis. Like the "force laws" of those two theories derive from the dimensionality of space time, the symmetry group involved (which is itself just an irreducible representation of rotations in the spacetime) and then some details having to do with symmetry breaking and the fact that gluons carry charge. Not that all of that is simple, but it doesn't invalidate the logic which gives us the 1/r^2 force law in the classical regimes of gravity and E&M.